I suppose

The vectors that span
form a basis for
if they are (1) linearly independent and (2) any vector in
can be expressed as a linear combination of those vectors (i.e. they span
).
Compute the Wronskian determinant:

The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of
is 3.
Write an arbitrary vector in
as
. Then the given vectors span
if there is always a choice of scalars
such that

which is equivalent to the system

The coefficient matrix is non-singular, so it has an inverse. Multiplying both sides by that inverse gives

so the vectors do span
.
The vectors comprising
form a basis for it because they are linearly independent.
Answer:
54 mph
Step-by-step explanation:
The interest due on the first payment is
.. I = Prt
.. I = 110,000*.055*(1/12)
.. I = 504.17
Then the decrease in principal resulting from the first payment is
.. 568.00 -504.17 = 63.83
and the new balance is
.. $110,000.00 -63.83 = $109,936.17
<u>Answer:</u>
x = 4 (extraneous solution)
<u>Step-by-step explanation:</u>

This solution is extraneous. Reason being that even if it can be solved algebraically, it is still not a valid solution because if we substitute back
, we will get two fractions with zero denominator which would be undefined.